Shadesmooth visible in solid view but not in rendered view
Technical Details

The problem is not with the normals nor with the smooth shading. It is the result of the algorithm in the ray tracing engine used to determine lighting. Set the size of the sun to zero, and you will see one sharp line between the lit and dark area. Basically, the calculated normals would suggest that the surfaces should be lit, however geometrically the surface is facing away from the light, so the lighting will not be caluclated.

Possible Solution

Generally such biases are always present for smooth shaded meshes, simply because the surface is only approximated with polygons. The better the approximation, the less these glitches appear.

In you case, the problem is, that there are 90 degrees sharp edges shaded smooth. Those are not really realistic either. You could make them sharp either via Properties Panel / Mesh / Normals / Auto Smooth or by adding an Edge Split modifer.

Here is the issue isolated and the Edge Split added: